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The variation of peak loads with tributary area near corners on flat low building roofs
Journal of Wind Engineering and Industrial Aerodynamics 77&78 (1998) 185—196
The variation of peak loads with tributary area near corners on flat low building roofs J.X. Lin*, D. Surry Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, London, Ontario, Canada N6A 5B9
Abstract This paper discusses the effect of spatial averaging of roof pressures on peak loads over various tributary areas near the corner of flat-top low-rise buildings. Simultaneous time series of pressures measured at locations within the corner region were used for analysis to form new time series of up-lift loads by instantaneous spatial averaging, for various building heights and plan dimensions. The variations of effective peak loads with location, shape and area, as well as with building dimensions, are presented and compared with those currently recommended for the corner zone by building codes, such as NBCC 1995 and ASCE 7-93. For areas including the corner point, the load reduces rapidly with increasing tributary area from the very high local peak value at the corner. The results demonstrate that the relationship between the effective load and tributary area is insensitive to the building dimensions if area is normalized by H where H is the building height, and is only slightly dependent on the shape of the areas that include the corner point. From an aerodynamic point of view, for buildings with plan dimensions larger than the height, the roof zoning by building codes should be based on H, and the specified load should be related to tributary areas normalized by H. 1998 Elsevier Science Ltd. All rights reserved. Keywords: Wind; Load; Pressure; Roof; Low-rise; Building; Tributary area; Aerodynamics
1. Introduction For low-rise buildings with flat or nearly flat roofs, wind-induced pressures in roof interior areas have become relatively well understood through a series of comprehensive studies over more than a decade (see e.g. Refs. [1—4]). Up-lift load values specified by building codes, such as NBCC 1995 [5] and ASCE 7-93 [6], have reflected these * Correspondence address. Applied Research Associates. Inc., Suite 100, 811 Spring Forest Rd, Raleigh, NC 27609, USA. 0167-6105/98/$ — see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 1 4 2 - 1
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results within a simplified format, although there is still some controversy over the use of the 0.8 factor in the Canadian codification, which allows for various effects, including those due to terrain uncertainties, variations in immediate surroundings, effects of wind directionality, etc. [7]. Compared to the interior region, there have been more uncertainties associated with the pressures near roof corners where normally the most severe wind loading is found. Recent experiments in both wind tunnel and full-scale have indicated very large peak suctions along the trace of the corner vortices for cornering wind angles attacking low buildings with flat or nearly flat roofs (see e.g., Refs. [8—11]); however, the relevance of these peak excursions to design have not been fully explored. It is the aim of this paper to make a contribution in this regard. Experiments previously carried out at the Boundary Layer Wind Tunnel Laboratory of the University of Western Ontario have included a family of low buildings whose geometries have progressed from the full-scale Texas Tech University test building shape to a generic flat-roof building of variable height with an extended afterbody, as sketched in Fig. 1. Previously reported results [11] indicate clearly that, near corners of flat roofs on which the flow is re-attaching, the patterns of pressure recorded are similar so long as the location relative to the corner is defined
Fig. 1. Illustration of the models and the details of the instrumented module.
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non-dimensionally in terms of the height of the building, and the oncoming flow characteristics are similar. The database described above has been re-examined the variation of effective peak pressure with tributary area. Averaging effects considered in this paper have been restricted to those of simple geometrical averaging. A future study will examine the effects of spatial averaging using influence surfaces from selected structural systems; however, the trends are expected to be similar for many structural effects. In either case, the spatial averaging effect is what is required to assess the importance of these unusual peak suctions to real design problems. Comparisons of the results with currently suggested variations of load with tributary area are included.
2. The experimental pressure data The data were developed using an electronically scanned system which measured the pressures essentially simultaneously at the 82 locations shown on the plan view of the instrumented module sketched in Fig. 1. This module was used in the corner of a series of 1 : 50 scale models designed to explore the similarity of the aerodynamics of the corner in open-country flow conditions. The starting point was the TTU full-scale experimental building modelled with its shallow roof angle, progressing to an otherwise geometrically similar flat-roofed model, and then to a series of flat-roofed models with large plan extensions to explore the influence of the “afterbody” on the pressures in the corners, and to explore the effects of height. The models and test techniques are described in detail in Ref. [11] where it is shown that the pressures near the corner collapse remarkably well when based on a normalized distance using the building height. This is thought to be generally true for rectangular flat roofs with plan dimensions larger than height, under similar conditions. It was also demonstrated that the TTU full-scale observations of very high peak suctions occurred on the trace of the vortex emanating from the corner. The models underestimated the worst full-scale peak pressure coefficient (C C ) of around !12, measured with a convenN E tional 8 mm diameter tap at “Location 50501” (1.4 m from one edge, 0.35 m from the other) [8,9], by roughly 33% but agreed better with the full-scale value of about !10 measured using an 80 mm “Super Pressure Tap” at the same location [12]. This indicates that the unmatched tap size is a major factor among the many that result in the model/full-scale discrepancies observed. At locations away from the vortex trace, agreement between model and full scale is generally excellent. The models also demonstrated that much more severe values occur on the vortex trace closer to the corner (where the full scale TTU building is uninstrumented). At the closest non-dimensional radial distance of 0.026H, or x"6 mm and y"1.5 mm on the highest model, a peak coefficient, C C (referenced to mean roof height dynamic N E pressure) of !18.5 was recorded. An example of these measured extreme peaks, is plotted as part of its time history of Fig. 2, scaled to a full-scale mean hourly roof height wind speed of 40 m/s, which is roughly comparable to Hurricane Andrew conditions. It can be seen that the duration of the peak is only a couple of seconds.
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Fig. 2. Time histories of pressure coefficients on a local tap location and of a 0.56 m tributary area containing the tap, full-scale building dimension: H"12 m;40 m;40 m, wind angle"25°.
Code-specified values in these corner regions are typically of the order of !5.4 [5], but are also suggested for tributary areas of the order of a square metre or less. Clearly, these very large experimental values suggest that such code provisions be carefully reviewed; however, it is not clear as to exactly what the implications are of these high experimental values for design. Design loads should recognize a number of factors beyond the simple extreme value at one location on an experimental model. Primary among these factors is that these highly fluctuating pressures are not necessarily well-correlated over larger areas and they often occur in regions where there are also strong spatial gradients. The time history of the area-averaged C for N a rectangular tributary area of 0.56 m containing the above locations is also shown in Fig. 2 for comparison. It can be seen that the peak at the corresponding time reduces to about !10.
3. Peak pressures for various tributary areas The experimental database of pressure time series referred to above has been corrected for residual non-simultaneity and digitally filtered at about 10 Hz full-scale, and re-examined to calculate the effective loads on various tributary areas. For simplicity, this has initially been carried out through averaging of available data over small areas (0.375 m;0.375 m) on various locations within the corner region, and over successively larger areas including the corner point. This results in new time histories of spatially averaged pressures for the specified areas. These account for both spatial variation and correlation effects. Their only limitation is the assumption of the fraction of the area, or weighting associated with each tap in the averaged area (simple
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area-fraction weighting has been used for all tributary areas containing several taps; for the results in Fig. 3, which includes some small inner areas containing no taps, a proximity weighting technique using the nearest 3—6 taps was adopted as a method of interpolation). The new time histories were produced for each tributary area considered and for each of the test wind angles of 0°, 15°, 25°, 30°, 35°, 45°, 55°, 60°, 65°, 75°, 90°. A number of different schemes for area averaging were considered as follows: (1) small square areas at various locations within the corner zone (see Fig. 3); (2) square areas, with one vertex at the corner and two sides along the aerodynamic corner edges (Fig. 4); (3) right triangular areas, with one vertex at the corner, one side along the edge, and another side along the 45° diagonal (Fig. 5); (4) 1 : 4 rectangular, geometrically similar areas (Fig. 6); (5) data from (2)—(4) plotted together (Fig. 7); (6) areas chosen to form a ragged approximation to the vortex trace (at about 14° to one edge) (Fig. 8). In Figs. 3—8, the results represent the worst peak coefficient, C C , referenced to N E mean roof height dynamic pressure, found over all tested wind directions. Each bar value in Fig. 3 is for the area and location defined by the X—½ plane while each data point in Figs. 4—8 is for the particular area indicated on the abscissa. These peak values are those derived by the Gumbel Type I extreme value method (using a Leiblein fit to the peaks of 10 segmental time histories) instead of the single peak directly taken from the time series. The results have also been factored by 0.8 to make them directly comparable to specified values in the National Building Code of Canada (NBCC). This is discussed further below.
4. Discussion Fig. 3 simply shows the variation with location of C C for 0.375 m;0.375 m N E tributary areas for the three large buildings with different heights. Increased magnitudes of C C are observed with increasing height while their distribution shapes are N E similar. The results for the successively larger square areas including the corner point are shown in Fig. 4. Fig. 4a shows the peak coefficients plotted versus area, and indicates quite a different behaviour for the various heights of buildings. For reference, the values suggested in NBCC 1995 and ASCE 7-93 are also shown (the ASCE 7-93 data have been converted from the values specified for fastest-mile reference wind speeds). These tend to be in fair agreement for larger areas at the right-end of the graph while it is clear that, in the current format adopted by at least these two codes, a single code-specified relationship between the load and area has difficulty reflecting the reality, particularly for smaller areas near the corner. Fig. 4b shows the same results plotted versus area normalized by H. Clearly, as also found for the local peaks [11], these tributary area loads correlate extremely well with H and strongly suggest that code specifications, at least for roof corner areas on flat-top low buildings, should be
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Fig. 3. Variation of tributary area loads with locations within the corner region for small square tributary areas of 0.375 m;0.375 m. (a) H"12 m;40 m;40 m; (b) H"8 m;40 m;40 m; (c) H"4 m;40 m;40 m.
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Fig. 4. Variation of tributary area loads with area for square tributary areas containing the corner point. (a) Area in absolute units; (b) area normalized by H.
specified in the same way. The corresponding mean C values also collapse, as shown N in Fig. 4b. Strong correlation between roof loads and the building height has also been indicated by the experimental results in Ref. [2] for larger roof areas including the interior region. This, combined with the results here, demonstrates that roof
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Fig. 5. Variation of tributary area loads with area for right triangular tributary areas containing the corner point.
Fig. 6. Variation of tributary area loads with area for rectangular tributary areas containing the corner point.
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Fig. 7. Variation of tributary area loads with area for various tributary area shapes.
Fig. 8. Illustration of tributary area loads varying with area following the vortex trace.
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zoning for load specification should also be expressed based on the coordinates normalized by H. In examining the data in Fig. 4, it should be noted that the smallest area data are those for the single tap closest to the corner, plotted against the tap area itself. All other areas contain a minimum of six taps. Figs. 5 and 6 inclusive show similar results for different tributary area shapes. Each contains a fit to the data of Fig. 4b for reference only. The similarity of the behaviours suggests that the precise shape of the tributary area in this region is not a strong effect. This can be more efficiently demonstrated in Fig. 7 where data from Figs. 4—6 are plotted all together. An approximate upper bound envelope curve for all the data presented in this figure is also shown. Finally, Fig. 8 displays the effect of increasing tributary areas that roughly follow the trace of the vortex and also include the corner point. The behaviour of these data, taken along the vortex trace, should be indicative of the smallest expected reduction in loading with increasing tributary area, although the tributary area considered is not particularly realistic with respect to any underlying structural system. The envelope curve from Fig. 7 is included. The comparison indicates that the rate of reduction of load with tributary area is not unduly sensitive to the particular areas chosen in the corner region. In Figs. 4—8, the results shown are the factored worst results over the range of tested angles. Generally, the worst results near the vortex trace originate from wind angles of around 30° and 60° with a progression towards wind angles of 0° and 90° for edge regions away from the corner. Examples of the peak C values versus wind angle are N shown in Fig. 9 for three different tributary areas: Fig. 9a contains data for square areas and Fig. 9b for rectangular areas. These are unfactored results. Each of these sets of data have been combined with an ominidirectional (circular) Rayleigh wind distribution to determine effective C C values, which are also shown as dotted lines in N E Fig. 9. These calculations follow the same methodology as detailed in Ref. [4]. For the azimuthal region beyond 0° or 90°, a conservative value equal to the larger of the values measured at 0° or 90° was assumed. The ratios of effective C C to worst case N E peak values are in the range of 0.77—0.87. Considering that the 0.8 factor is based on reductions attributable to a variety of factors, of which directionality is only one [7], the above ratios are quite consistent with the overall 0.8 factor adopted in the NBCC.
5. Concluding remarks In the region near the roof corner of low-rise buildings (plan dimensions of the order of 1.0H or more), the specified coefficients should be related to tributary areas normalized by H. The resulting relationship between specified coefficient and area is then independent of building dimensions and relatively insensitive to the shape of area within the corner region, so long as it includes the corner point. In this region, loads reduce rapidly with increasing tributary area; an area of 0.1H;0.1H is about a factor of 2 less than the local peak.
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Fig. 9. Illustration of the effect of directionality on effective H"12 m;40 m;40 m. (a) Square areas; (b) rectangular areas.
loads,
building
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dimensions:
Similar experimental data are also available for areas away from the corner, and similar analyses are planned to extend these results to other roof regions. Effects of actual structural influence functions to determine the effective loads on typical roof systems and their variation with tributary area will also be explored.
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References [1] T. Stathopoulos, Turbulent wind action on low rise building, Ph. D. Thesis, Faculty of Engineering Science, University of Western Ontario, London, Ontario, Canada, 1979. [2] D. Surry, E.M.F. Stopar, Wind loading of large low buildings, Can. J. Civil Eng. 16 (1989) 526—542. [3] T.C.E. Ho, D. Surry, A.G. Davenport, Variability of low building wind loads due to surroundings, J. Wind Eng. Ind. Aerodyn. 38 (1991) 297—310. [4] T.C.E. Ho, A.G. Davenport, D. Surry, Characteristic pressure distribution shapes and load repetitions for the wind loading of low building roof panels, J. Wind Eng. Ind. Aerodyn. 57 (1995) 261—279. [5] Canadian Commission on Building and Fire Codes, National Building Code Canada 1995, Structural Commentaries (Part 4), NRCC No. 38826, Institute for Research in Construction, National Research Council of Canada, 1996. [6] American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures, ASCE 7-93, 1993. [7] A.G. Deavenport, T.C.E. Ho, D. Surry, The codification of low building wind loads, Proc. 7th US National Conf. on Wind Engineering, Los Angeles, 27—30 June 1993. [8] K.C. Mehta, M.L. Levitan, Roof corner pressures measured in the field on a low building, J. Wind Eng. Ind. Aerodyn. 41 (1992) 181—192. [9] L.S. Cochran, J.E. Cermak, Full- and model-scale cladding pressures on the Texas Tech Experimental Building, J. Wind Eng. Ind. Aerodyn. 43 (1992) 1589—1600. [10] R.V. Milford, A.M. Goliger, J.L. Waldech, Jan Smuts experiment: comparison of full-scale and wind-tunnel results, J. Wind Eng. Ind. Aerodyn. 43 (1992) 1693—1704. [11] J.X. Lin, D. Surry, H.W. Tieleman, The distribution of pressure near roof corners of flat roof low buildings, J. Wind Eng. Ind. Aerodyn. 56 (1995) 235—265. [12] L.S. Cochran, M.L. Levitan, J.E. Cermak, B.B. Yeatts, Geometric similitude applied to model and full-scale pressure tap sizes, Proc. 3rd Asia-Pacific Symp. on Wind Eng., Hong Kong, 13—15 December 1993.
The variation of peak loads with tributary area near corners on flat low building roofs J.X. Lin*, D. Surry Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, London, Ontario, Canada N6A 5B9
Abstract This paper discusses the effect of spatial averaging of roof pressures on peak loads over various tributary areas near the corner of flat-top low-rise buildings. Simultaneous time series of pressures measured at locations within the corner region were used for analysis to form new time series of up-lift loads by instantaneous spatial averaging, for various building heights and plan dimensions. The variations of effective peak loads with location, shape and area, as well as with building dimensions, are presented and compared with those currently recommended for the corner zone by building codes, such as NBCC 1995 and ASCE 7-93. For areas including the corner point, the load reduces rapidly with increasing tributary area from the very high local peak value at the corner. The results demonstrate that the relationship between the effective load and tributary area is insensitive to the building dimensions if area is normalized by H where H is the building height, and is only slightly dependent on the shape of the areas that include the corner point. From an aerodynamic point of view, for buildings with plan dimensions larger than the height, the roof zoning by building codes should be based on H, and the specified load should be related to tributary areas normalized by H. 1998 Elsevier Science Ltd. All rights reserved. Keywords: Wind; Load; Pressure; Roof; Low-rise; Building; Tributary area; Aerodynamics
1. Introduction For low-rise buildings with flat or nearly flat roofs, wind-induced pressures in roof interior areas have become relatively well understood through a series of comprehensive studies over more than a decade (see e.g. Refs. [1—4]). Up-lift load values specified by building codes, such as NBCC 1995 [5] and ASCE 7-93 [6], have reflected these * Correspondence address. Applied Research Associates. Inc., Suite 100, 811 Spring Forest Rd, Raleigh, NC 27609, USA. 0167-6105/98/$ — see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 1 4 2 - 1
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results within a simplified format, although there is still some controversy over the use of the 0.8 factor in the Canadian codification, which allows for various effects, including those due to terrain uncertainties, variations in immediate surroundings, effects of wind directionality, etc. [7]. Compared to the interior region, there have been more uncertainties associated with the pressures near roof corners where normally the most severe wind loading is found. Recent experiments in both wind tunnel and full-scale have indicated very large peak suctions along the trace of the corner vortices for cornering wind angles attacking low buildings with flat or nearly flat roofs (see e.g., Refs. [8—11]); however, the relevance of these peak excursions to design have not been fully explored. It is the aim of this paper to make a contribution in this regard. Experiments previously carried out at the Boundary Layer Wind Tunnel Laboratory of the University of Western Ontario have included a family of low buildings whose geometries have progressed from the full-scale Texas Tech University test building shape to a generic flat-roof building of variable height with an extended afterbody, as sketched in Fig. 1. Previously reported results [11] indicate clearly that, near corners of flat roofs on which the flow is re-attaching, the patterns of pressure recorded are similar so long as the location relative to the corner is defined
Fig. 1. Illustration of the models and the details of the instrumented module.
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non-dimensionally in terms of the height of the building, and the oncoming flow characteristics are similar. The database described above has been re-examined the variation of effective peak pressure with tributary area. Averaging effects considered in this paper have been restricted to those of simple geometrical averaging. A future study will examine the effects of spatial averaging using influence surfaces from selected structural systems; however, the trends are expected to be similar for many structural effects. In either case, the spatial averaging effect is what is required to assess the importance of these unusual peak suctions to real design problems. Comparisons of the results with currently suggested variations of load with tributary area are included.
2. The experimental pressure data The data were developed using an electronically scanned system which measured the pressures essentially simultaneously at the 82 locations shown on the plan view of the instrumented module sketched in Fig. 1. This module was used in the corner of a series of 1 : 50 scale models designed to explore the similarity of the aerodynamics of the corner in open-country flow conditions. The starting point was the TTU full-scale experimental building modelled with its shallow roof angle, progressing to an otherwise geometrically similar flat-roofed model, and then to a series of flat-roofed models with large plan extensions to explore the influence of the “afterbody” on the pressures in the corners, and to explore the effects of height. The models and test techniques are described in detail in Ref. [11] where it is shown that the pressures near the corner collapse remarkably well when based on a normalized distance using the building height. This is thought to be generally true for rectangular flat roofs with plan dimensions larger than height, under similar conditions. It was also demonstrated that the TTU full-scale observations of very high peak suctions occurred on the trace of the vortex emanating from the corner. The models underestimated the worst full-scale peak pressure coefficient (C C ) of around !12, measured with a convenN E tional 8 mm diameter tap at “Location 50501” (1.4 m from one edge, 0.35 m from the other) [8,9], by roughly 33% but agreed better with the full-scale value of about !10 measured using an 80 mm “Super Pressure Tap” at the same location [12]. This indicates that the unmatched tap size is a major factor among the many that result in the model/full-scale discrepancies observed. At locations away from the vortex trace, agreement between model and full scale is generally excellent. The models also demonstrated that much more severe values occur on the vortex trace closer to the corner (where the full scale TTU building is uninstrumented). At the closest non-dimensional radial distance of 0.026H, or x"6 mm and y"1.5 mm on the highest model, a peak coefficient, C C (referenced to mean roof height dynamic N E pressure) of !18.5 was recorded. An example of these measured extreme peaks, is plotted as part of its time history of Fig. 2, scaled to a full-scale mean hourly roof height wind speed of 40 m/s, which is roughly comparable to Hurricane Andrew conditions. It can be seen that the duration of the peak is only a couple of seconds.
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Fig. 2. Time histories of pressure coefficients on a local tap location and of a 0.56 m tributary area containing the tap, full-scale building dimension: H"12 m;40 m;40 m, wind angle"25°.
Code-specified values in these corner regions are typically of the order of !5.4 [5], but are also suggested for tributary areas of the order of a square metre or less. Clearly, these very large experimental values suggest that such code provisions be carefully reviewed; however, it is not clear as to exactly what the implications are of these high experimental values for design. Design loads should recognize a number of factors beyond the simple extreme value at one location on an experimental model. Primary among these factors is that these highly fluctuating pressures are not necessarily well-correlated over larger areas and they often occur in regions where there are also strong spatial gradients. The time history of the area-averaged C for N a rectangular tributary area of 0.56 m containing the above locations is also shown in Fig. 2 for comparison. It can be seen that the peak at the corresponding time reduces to about !10.
3. Peak pressures for various tributary areas The experimental database of pressure time series referred to above has been corrected for residual non-simultaneity and digitally filtered at about 10 Hz full-scale, and re-examined to calculate the effective loads on various tributary areas. For simplicity, this has initially been carried out through averaging of available data over small areas (0.375 m;0.375 m) on various locations within the corner region, and over successively larger areas including the corner point. This results in new time histories of spatially averaged pressures for the specified areas. These account for both spatial variation and correlation effects. Their only limitation is the assumption of the fraction of the area, or weighting associated with each tap in the averaged area (simple
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area-fraction weighting has been used for all tributary areas containing several taps; for the results in Fig. 3, which includes some small inner areas containing no taps, a proximity weighting technique using the nearest 3—6 taps was adopted as a method of interpolation). The new time histories were produced for each tributary area considered and for each of the test wind angles of 0°, 15°, 25°, 30°, 35°, 45°, 55°, 60°, 65°, 75°, 90°. A number of different schemes for area averaging were considered as follows: (1) small square areas at various locations within the corner zone (see Fig. 3); (2) square areas, with one vertex at the corner and two sides along the aerodynamic corner edges (Fig. 4); (3) right triangular areas, with one vertex at the corner, one side along the edge, and another side along the 45° diagonal (Fig. 5); (4) 1 : 4 rectangular, geometrically similar areas (Fig. 6); (5) data from (2)—(4) plotted together (Fig. 7); (6) areas chosen to form a ragged approximation to the vortex trace (at about 14° to one edge) (Fig. 8). In Figs. 3—8, the results represent the worst peak coefficient, C C , referenced to N E mean roof height dynamic pressure, found over all tested wind directions. Each bar value in Fig. 3 is for the area and location defined by the X—½ plane while each data point in Figs. 4—8 is for the particular area indicated on the abscissa. These peak values are those derived by the Gumbel Type I extreme value method (using a Leiblein fit to the peaks of 10 segmental time histories) instead of the single peak directly taken from the time series. The results have also been factored by 0.8 to make them directly comparable to specified values in the National Building Code of Canada (NBCC). This is discussed further below.
4. Discussion Fig. 3 simply shows the variation with location of C C for 0.375 m;0.375 m N E tributary areas for the three large buildings with different heights. Increased magnitudes of C C are observed with increasing height while their distribution shapes are N E similar. The results for the successively larger square areas including the corner point are shown in Fig. 4. Fig. 4a shows the peak coefficients plotted versus area, and indicates quite a different behaviour for the various heights of buildings. For reference, the values suggested in NBCC 1995 and ASCE 7-93 are also shown (the ASCE 7-93 data have been converted from the values specified for fastest-mile reference wind speeds). These tend to be in fair agreement for larger areas at the right-end of the graph while it is clear that, in the current format adopted by at least these two codes, a single code-specified relationship between the load and area has difficulty reflecting the reality, particularly for smaller areas near the corner. Fig. 4b shows the same results plotted versus area normalized by H. Clearly, as also found for the local peaks [11], these tributary area loads correlate extremely well with H and strongly suggest that code specifications, at least for roof corner areas on flat-top low buildings, should be
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Fig. 3. Variation of tributary area loads with locations within the corner region for small square tributary areas of 0.375 m;0.375 m. (a) H"12 m;40 m;40 m; (b) H"8 m;40 m;40 m; (c) H"4 m;40 m;40 m.
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Fig. 4. Variation of tributary area loads with area for square tributary areas containing the corner point. (a) Area in absolute units; (b) area normalized by H.
specified in the same way. The corresponding mean C values also collapse, as shown N in Fig. 4b. Strong correlation between roof loads and the building height has also been indicated by the experimental results in Ref. [2] for larger roof areas including the interior region. This, combined with the results here, demonstrates that roof
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Fig. 5. Variation of tributary area loads with area for right triangular tributary areas containing the corner point.
Fig. 6. Variation of tributary area loads with area for rectangular tributary areas containing the corner point.
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Fig. 7. Variation of tributary area loads with area for various tributary area shapes.
Fig. 8. Illustration of tributary area loads varying with area following the vortex trace.
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zoning for load specification should also be expressed based on the coordinates normalized by H. In examining the data in Fig. 4, it should be noted that the smallest area data are those for the single tap closest to the corner, plotted against the tap area itself. All other areas contain a minimum of six taps. Figs. 5 and 6 inclusive show similar results for different tributary area shapes. Each contains a fit to the data of Fig. 4b for reference only. The similarity of the behaviours suggests that the precise shape of the tributary area in this region is not a strong effect. This can be more efficiently demonstrated in Fig. 7 where data from Figs. 4—6 are plotted all together. An approximate upper bound envelope curve for all the data presented in this figure is also shown. Finally, Fig. 8 displays the effect of increasing tributary areas that roughly follow the trace of the vortex and also include the corner point. The behaviour of these data, taken along the vortex trace, should be indicative of the smallest expected reduction in loading with increasing tributary area, although the tributary area considered is not particularly realistic with respect to any underlying structural system. The envelope curve from Fig. 7 is included. The comparison indicates that the rate of reduction of load with tributary area is not unduly sensitive to the particular areas chosen in the corner region. In Figs. 4—8, the results shown are the factored worst results over the range of tested angles. Generally, the worst results near the vortex trace originate from wind angles of around 30° and 60° with a progression towards wind angles of 0° and 90° for edge regions away from the corner. Examples of the peak C values versus wind angle are N shown in Fig. 9 for three different tributary areas: Fig. 9a contains data for square areas and Fig. 9b for rectangular areas. These are unfactored results. Each of these sets of data have been combined with an ominidirectional (circular) Rayleigh wind distribution to determine effective C C values, which are also shown as dotted lines in N E Fig. 9. These calculations follow the same methodology as detailed in Ref. [4]. For the azimuthal region beyond 0° or 90°, a conservative value equal to the larger of the values measured at 0° or 90° was assumed. The ratios of effective C C to worst case N E peak values are in the range of 0.77—0.87. Considering that the 0.8 factor is based on reductions attributable to a variety of factors, of which directionality is only one [7], the above ratios are quite consistent with the overall 0.8 factor adopted in the NBCC.
5. Concluding remarks In the region near the roof corner of low-rise buildings (plan dimensions of the order of 1.0H or more), the specified coefficients should be related to tributary areas normalized by H. The resulting relationship between specified coefficient and area is then independent of building dimensions and relatively insensitive to the shape of area within the corner region, so long as it includes the corner point. In this region, loads reduce rapidly with increasing tributary area; an area of 0.1H;0.1H is about a factor of 2 less than the local peak.
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Fig. 9. Illustration of the effect of directionality on effective H"12 m;40 m;40 m. (a) Square areas; (b) rectangular areas.
loads,
building
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dimensions:
Similar experimental data are also available for areas away from the corner, and similar analyses are planned to extend these results to other roof regions. Effects of actual structural influence functions to determine the effective loads on typical roof systems and their variation with tributary area will also be explored.
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References [1] T. Stathopoulos, Turbulent wind action on low rise building, Ph. D. Thesis, Faculty of Engineering Science, University of Western Ontario, London, Ontario, Canada, 1979. [2] D. Surry, E.M.F. Stopar, Wind loading of large low buildings, Can. J. Civil Eng. 16 (1989) 526—542. [3] T.C.E. Ho, D. Surry, A.G. Davenport, Variability of low building wind loads due to surroundings, J. Wind Eng. Ind. Aerodyn. 38 (1991) 297—310. [4] T.C.E. Ho, A.G. Davenport, D. Surry, Characteristic pressure distribution shapes and load repetitions for the wind loading of low building roof panels, J. Wind Eng. Ind. Aerodyn. 57 (1995) 261—279. [5] Canadian Commission on Building and Fire Codes, National Building Code Canada 1995, Structural Commentaries (Part 4), NRCC No. 38826, Institute for Research in Construction, National Research Council of Canada, 1996. [6] American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures, ASCE 7-93, 1993. [7] A.G. Deavenport, T.C.E. Ho, D. Surry, The codification of low building wind loads, Proc. 7th US National Conf. on Wind Engineering, Los Angeles, 27—30 June 1993. [8] K.C. Mehta, M.L. Levitan, Roof corner pressures measured in the field on a low building, J. Wind Eng. Ind. Aerodyn. 41 (1992) 181—192. [9] L.S. Cochran, J.E. Cermak, Full- and model-scale cladding pressures on the Texas Tech Experimental Building, J. Wind Eng. Ind. Aerodyn. 43 (1992) 1589—1600. [10] R.V. Milford, A.M. Goliger, J.L. Waldech, Jan Smuts experiment: comparison of full-scale and wind-tunnel results, J. Wind Eng. Ind. Aerodyn. 43 (1992) 1693—1704. [11] J.X. Lin, D. Surry, H.W. Tieleman, The distribution of pressure near roof corners of flat roof low buildings, J. Wind Eng. Ind. Aerodyn. 56 (1995) 235—265. [12] L.S. Cochran, M.L. Levitan, J.E. Cermak, B.B. Yeatts, Geometric similitude applied to model and full-scale pressure tap sizes, Proc. 3rd Asia-Pacific Symp. on Wind Eng., Hong Kong, 13—15 December 1993.